Data Sufficiency Pack 1, Question 3) If a, b and c are integers...

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QUANT 4-PACK SERIES Data Sufficiency Pack 1 Question 3 If a, b and c are integers...

If a, b and c are integers and abc is an even integer, is b an odd integer?

1) ab + bc + ac is an even integer
2) a + c is an odd integer

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This question is part of the Quant 4-Pack series

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ENGRTOMBA2018 · Answer

Given a,b,c are integers and abc= even, b = odd?

Per statement 1, 2ab+bc = e ---> b(2a+c) = e ---> 3 cases

Case 1, b=e , 2a+c=o , "Yes"

Case 2, b=o, 2a+c=e, "No"

Cae 3, b=e, 2a+c=e, "Yes"

Thus not sufficient.

Statement 2, a+c=o --> 2 cases

Case 1, a=o and c=e ---> b=even or odd to give abc=even , making this statement clearly not sufficient. You can stop here.

Case 2, not required.

Combining, you get,

a+c=o and abc = even, possible cases

from statement 2,
a b c
o o e
o e e
e o o
e e o

and from statement 1,

a b c
o e e
e e e
o e o
e e o
o o e
e o e

Thus the cases common are:

a b c
o o e
o e e
e e o

Making E the correct answer for "is b =odd"

musunna · Answer

Given that abc = Even integer. So  at least 1 of the 3 integers is Even .
Question asks  whether B = ODD ?

Statement 1  says ab + bc + ab is an even integer. So b * (2a+c) = Even.  So either b OR (2a+c) is even .  NOT sufficient .
 Statement 2  says a+c = ODD Integer. i.e.  So either a OR c is ODD . So there is no inference of b.  NOT sufficient .

Combining Statement 1 & 2 , There is no definite answer for b. Both odd & even value of b satisfy the conditions.

So option (E) wins.

EMPOWERgmatRichC · Answer

Hi All,

Unfortunately, the original prompt had a typo in it (it's since been 'fixed'); the first two responses to the question were correct for the question that was originally posted. Here is the explanation for the updated question.

We're told that A, B and C are integers and that ABC is EVEN. We're asked if B is EVEN. This is a YES/NO question. The prompt can be solved with a combination of Number Property rules and TESTing VALUES (if needed).

From the prompt, we know that ABC is even, so AT LEAST one of the three variables must be even (since an EVEN multiplied by any other integer(s) is EVEN).

1) AB + BC + AC is an even integer

With this Fact, there is more than one way to end up with an EVEN sum...

IF...
A = Even
B = Even
C = Even
(E)(E) + (E)(E) + (E)(E) = Even
Then the answer to the question is YES.

IF...
A = Even
B = Odd
C = Even
(E)(O) + (E)(E) + (E)(O) = Even
Then the answer to the question is NO.
Fact 1 is INSUFFICIENT

2) A + C is an odd integer

This Fact tells us that ONE of those two variables is EVEN and the other is ODD (since Even + Odd = Odd), but it tells us NOTHING about B. 
Fact 2 is INSUFFICIENT.

Combined, we know...
AB + BC + AC = Even
Between A and C, one is Even and the other is Odd

With these limitations, there are only two possibilities...

IF...
A = Even
B = Even
C = Odd
(E)(E) + (E)(O) + (E)(O) = Even
Then the answer to the question is YES.

IF...
A = Odd
B = Even
C = Even
(O)(E) + (E)(E) + (O)(E) = Even
Then the answer to the question is YES.

Combined, SUFFICIENT

Final Answer:  C

GMAT assassins aren't born, they're made,
Rich

Mo2men · Answer

Hi Rich,

Can you please fix the question to "is B an Even integer"? In your answer, when you combined both facts is always 'Yes', while the old prompt is still 'is B an Odd integer'.

This will help practitioners not to confuse and go back and forth between the original prompt and your answer.

Thanks

KrishnakumarKA1 · Answer

Prompt analysis
abc is even integer, that means either one or two of the integer or all three integers are even.

Superset
The answer will be either yes or no.

Translation
To find the answer, we need: 
1# exact value of a,b,c
2# the properties in terms of even/odd for a,b,c
3# three equations and three variables to find a,b,c.

Statement analysis
St 1: ab +bc +ac is even that means each of the term could be even +odd +odd or even +even +even. If a is even, that means ab and ac is even therefore even +odd+odd is ruled out. Hence all the term is even. I.e bc is even as well. But we cannot say is c is even or b is even. INSUFFICIENT

St 2: a +c is odd. Even +odd = odd. That means either a or c is even. Hence abc is even. But cannot say anything about b. INSUFFICIENT.

St 2 & St 1: from statement 2 we can say either a or c is even and the other is odd. Let us take a be even and c be odd. Hence ab and ac is even. From statement 1, we can say that bc is also even. If c is odd, b has to be even. ANSWER. Similarly, you can reverse a and c and you will get the same result.
Option C

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